Question

Find the perimeter of quadrilateral PQRS​ given that the coordinates of its vertices are

P(1,3)​,Q(3,1)​,R(1,−1)​, and S(−2,−1)​. You may round your answer to one decimal place.

Answer 1

`~\hfill \stackrel{\textit{\large distance between 2 points}}{d = √(( x_2- x_1)^2 + ( y_2- y_1)^2)}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ P(\stackrel{x_1}{1}~,~\stackrel{y_1}{3})\qquad Q(\stackrel{x_2}{3}~,~\stackrel{y_2}{1}) ~\hfill PQ=√((~~ 3- 1~~)^2 + (~~ 1- 3~~)^2) \\\\\\ ~\hfill PQ=√(( 2 )^2 + ( -2)^2) \implies \boxed{PQ=√( 8)}`

`Q(\stackrel{x_1}{3}~,~\stackrel{y_1}{1})\qquad R(\stackrel{x_2}{1}~,~\stackrel{y_2}{-1}) ~\hfill QR=√((~~ 1- 3~~)^2 + (~~ -1- 1 ~~)^2) \\\\\\ ~\hfill QR=√(( -2)^2 + ( -2)^2) \implies \boxed{QR=√( 8)} \\\\\\ R(\stackrel{x_1}{1}~,~\stackrel{y_1}{-1})\qquad S(\stackrel{x_2}{-2}~,~\stackrel{y_2}{-1}) ~\hfill RS=√((~~ -2- 1~~)^2 + (~~ -1- (-1)~~)^2) \\\\\\ ~\hfill RS=√(( -3)^2 + ( 0)^2) \implies RS=√( 9)\implies \boxed{RS=3}`

`S(\stackrel{x_1}{-2}~,~\stackrel{y_1}{-1})\qquad P(\stackrel{x_2}{1}~,~\stackrel{y_2}{3}) ~\hfill SP=√((~~ 1- (-2)~~)^2 + (~~ 3- (-1)~~)^2) \\\\\\ ~\hfill SP=√(( 3)^2 + ( 4)^2) \implies SP=√( 25)\implies \boxed{SP=5} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{\LARGE Perimeter} }{√(8)+√(8)+3+5} ~~ \approx ~~ \text{\LARGE 13.7}`